It is necessary to have, both roots and shoots on each division. If you are not able to do this, then the tuber is best left alone. This is a nutrient storage organ that is necessary for feeding the plants. If there is none left on the shoot, then it will likely die. Could you send a picture of what you are referring to so that I may help you to divide this correctly? For now, here is an article that will help: https://www.gardeningknowhow.com/ornamental/bulbs/dahlia/dividing-dahlia-tubers.htm